= Krull dimension criterion for rank-one generalized Weyl algebras
{c}
For a commutative Noetherian base $D$ of finite dimension $d$, the <noncommutative Krull dimension> of $D(\sigma,t)$ equals $d$ unless a height-$d$ maximal ideal is periodic under $\sigma$ or contains infinitely many translates $\sigma^n(t)$. This is the commutative-base specialization of Theorem 5.3 in https://webhomes.maths.ed.ac.uk/~tom/KdimGWA.pdf[Krull dimension of Generalized Weyl Algebras with non-commutative coefficients].
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